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Generative Large Language Models (LLMs) stand as a revolutionary advancement in the modern era of artificial intelligence (AI). However, scaling down LLMs for resource-constrained hardware, such as Internet-of-Things (IoT) devices requires non-trivial efforts and domain knowledge. In this paper, we propose a novel information-entropy framework for designing mobile-friendly generative language models. The whole design procedure involves solving a mathematical programming (MP) problem, which can be done on the CPU within minutes, making it nearly zero-cost. We evaluate our designed models, termed MeRino, across fourteen NLP downstream tasks, showing their competitive performance against the state-of-the-art autoregressive transformer models under the mobile setting. Notably, MeRino achieves similar or better performance on both language modeling and zero-shot learning tasks, compared to the 350M parameter OPT while being 4.9x faster on NVIDIA Jetson Nano with 5.5x reduction in model size.